Solve for $x$ and $y$ using elimination. ${-3x-2y = -33}$ ${-2x+2y = -2}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-5x = -35$ $\dfrac{-5x}{{-5}} = \dfrac{-35}{{-5}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-3x-2y = -33}\thinspace$ to find $y$ ${-3}{(7)}{ - 2y = -33}$ $-21-2y = -33$ $-21{+21} - 2y = -33{+21}$ $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {-2x+2y = -2}\thinspace$ and get the same answer for $y$ : ${-2}{(7)}{ + 2y = -2}$ ${y = 6}$